non-homogenous equation

[Yunqi(Yuki) Huang]

I wonder that how can we solve the problem when the right-hand side of the non-homogenous equation is only a constant?

[Victor Ivrii]

What equation?Linear? With constant coefficients? Read a textbook or follpw lectures

[Yunqi(Yuki) Huang]

I mean we usually solve the second order equation like y''+2y'+y= 2e^(-t), which right-hand side is a non-homogenous equation. We could assume right-hand side is Y(t)=Ae^(-t), then substitute y'' and y' and y in the ordinary equation. However, how can we solve the equation like y''+2y'+y=3? If it is right to assume Y(t)=A for the right-hand side?

[Wei Cui]

If the equation is a non-homogeneous and the right-hand side is a constant, I think you can assume that the particular solution $y(t) = at + b$ and try to solve the equation.

[Victor Ivrii]

I mean we usually solve the second order equation like y''+2y'+y= 2e^(-t), which right-hand side is a non-homogenous equation. We could assume right-hand side is Y(t)=Ae^(-t), then substitute y'' and y' and y in the ordinary equation. However, how can we solve the equation like y''+2y'+y=3? If it is right to assume Y(t)=A for the right-hand side?

YES, because $3=3e^{0x}$ and $r=0$ is not a characteristic root.